Theorems · Theorem · ring theory
Algebra.TensorProduct.includeLeft_bijective
∀ {R : Type uR} {S : Type uS} {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [inst_3 : Semiring A] [inst_4 : Algebra R A] [inst_5 : Algebra S A]
[inst_6 : IsScalarTower R S A] [inst_7 : Semiring B] [inst_8 : Algebra R B],
Function.Bijective ⇑(algebraMap R B) → Function.Bijective ⇑Algebra.TensorProduct.includeLeft- Defined in
- Mathlib.RingTheory.TensorProduct.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
- Function.Bijectivestatement and proof · cited by 863
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.Bijective.isStableUnderBaseChangeproof · cited by 0
- Algebra.TensorProduct.includeRight_bijectiveproof · cited by 0